Well, even though Paul was arguably the most literate person in his generation "advancing in Judaism ahead of all his peers" he still used a scribe to write many of his letters. Similarly, John Mark served as a scribe to write down what Peter had to say. Luke was a Greek from Troas, Turkey. John spent most of his last thirty years living in Ephesus, Turkey, no doubt speaking Greek. Revelation was addressed to seven Greek speaking churches in Turkey.
"Everybody" spoke Greek the way "everybody" speaks English in the world today in addition to their native languages. So it was entirely natural for the letters and gospels to be written in the official international language of that day - especially when most of them were addressed to people outside Judea.
Since the apostles were given the Great Commission by Jesus to "make disciples of all nations", it would not make any sense have chosen to do that in Hebrew or Aramaic anyway.
Even the Old Testament had been independently translated into Greek (Septuagint) by 72 Jewish Scholars commissioned by King Ptolemy of Egypt. It became the standard translation in use throughout the world for hundreds of years surrounding the time of Christ.